Question

A sequence can be generated by using an = 4a(n - 1)) where a= 6 and n is a whole

number greater than 1. What are the first four terms in the sequence?

Answer 1

Given:

The sequence can be generated by

`a_n=4a_((n - 1))`

Where
`a_1= 6` and
`n` is a whole number greater than 1.

To find:

The first four terms of the given sequence.

Solution:

We have,

`a_n=4a_((n - 1))` ...(i)

It is given that
`a_1= 6`. So, for
`n=2`, we get

`a_2=4a_((2 - 1))`

`a_2=4a_1`

`a_2=4(6)`

`a_2=24`

Putting
`n=3` in (i), we get

`a_3=4a_((3- 1))`

`a_3=4a_2`

`a_3=4(24)`

`a_3=96`

Putting
`n=4` in (i), we get

`a_4=4a_((4- 1))`

`a_4=4a_3`

`a_4=4(96)`

`a_4=384`

The first four terms of the given sequence are 6, 24, 96,384.

Therefore, the correct option is C.